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ABSTRACT
The present study investigates the effects of fluid thermo-physical property variations on fully developed turbulent mixed convection flow in vertical and horizontal parallel plate channels where walls are kept at different temperatures. The main attention is paid to the validity of the Boussinesq approximation when the temperature differences are enhanced. Reynolds number based on the channel half-width and friction velocity is assumed to be 150. The governing equations are solved utilizing the large eddy simulation and the low Mach number approach on a finite-volume basis. Dealing with the sub-grid scale stress tensor and the heat flux vector, the dynamic Smagorinsky model is used. All the numerical simulations are carried out by developing a solver in OpenFOAM. The present results display that an increase in the walls' temperature difference, applying the Boussinesq approximation and neglecting the dependency of thermal conductivity and dynamic viscosity on temperature, can result in relatively large errors. Deviations of up to 33% and 45% in the prediction of friction coefficient and Nusselt number, respectively, are shown. This is true for both vertical and horizontal configurations.
Nomenclature
| Bo | = | Boussinesq number, = ρref2cp2refgβΔT(2δ)3/kref2 |
| Cf | = | Friction coefficient, = 2τw/ρbub2 |
| cp | = | Specific heat at constant pressure, Jkg− 1K− 1 |
| Cs | = | Smagorinsky factor |
| Cθ | = | Smagorinsky heat flux vector factor |
| DNS | = | Direct numerical simulation |
| g | = | Acceleration due to gravity, ms− 2 |
| Gr | = | Grashof number, = ρref2gβΔT(2δ)3/μref2 |
| k | = | Thermal conductivity, Wm− 1K− 1 |
| L | = | Channel dimension, m |
| LES | = | Large eddy simulation |
| M | = | Mach number, |
| N | = | Number of cells |
| Nu | = | Nusselt number, = 4δqw/k(Tw − Tb) |
| p | = | Pressure, Pa |
| P | = | Dimensionless pressure |
| = | Peclet number, = RePr | |
| = | Prandtl number, = cpμref/kref | |
| q | = | Heat flux, = (k dT/dy), Wm− 2 |
| R | = | Constant of gases |
| = | Reynolds number, = 2ρrefubδ/μref | |
| = | Frictional Reynolds number, = ρrefuτδ/μref | |
| Sij | = | Strain rate tensor |
| td | = | Time, s |
| t | = | Dimensionless time |
| T | = | Temperature, K |
| Tm | = | Average temperature, K |
| Tτ | = | Frictional temperature, = qw /ρcpuτ |
| u, v, w | = | Velocity components, ms− 1 |
| uτ | = | Friction velocity, |
| u0 | = | Centerline velocity across the channel width, ms− 1 |
| U, V, W | = | Dimensionless velocity components |
| Urms, Vrms, Wrms | = | Dimensionless root-mean-square velocity components |
| Vo | = | Volume, m3 |
| x, y, z | = | Coordinates, m |
| X, Y, Z | = | Dimensionless Coordinates |
| Greek symbols | ||
| β | = | Volumetric expansion coefficient, = 1/((Th + Tc)/2), 1/K |
| δ | = | Channel half width, m |
| μ | = | Dynamic viscosity, N.s/m2 |
| μt | = | Sub-grid scale viscosity, N.s/m2 |
| γ | = | Grid development ratio |
| Φ | = | Any variable |
| θ | = | Dimensionless Temperature, = (T − Tc)/(Th − Tc) |
| ρ | = | Density, kgm− 3 |
| τ | = | Shear stress, = (μ du/dy), N/m2 |
| Y | = | Specific heat ratio |
| Δ | = | Filter width, m |
| σ | = | Stress, = (μ du/dy), N/m2 |
| Subscripts | ||
| b | = | Bulk value |
| OB, NOB | = | Oberbeck-Boussinesq and non-Oberbeck-Bouss-inesq conditions |
| c | = | Cold |
| h | = | Hot |
| cen | = | Centerline |
| thermo | = | Thermodynamic |
| i, j | = | Denoting x, y respectively. |
| x, y, z | = | Directions |
| ref | = | Reference value |
| rms | = | Root-mean-square value |
| m | = | Mean value |
| w | = | Wall value |
| τ | = | Quantity based on frictional velocity |
| Superscripts | ||
| ― | = | Space filtered value |
| ∼ | = | Favre-filtered value |
| + | = | Wall units |
| ˆ | = | Second-filtered value |
| sgs | = | Sub-grid scale |
| a | = | Deviatoric part |
Additional information
Notes on contributors
Farzad Bazdidi-Tehrani
Farzad Bazdidi-Tehrani completed his M.S. and Ph.D. degrees at Leeds University, UK. He joined the School of Mechanical Engineering at Iran University of Science and Technology in 1991 and since then has been active in both teaching and research. He has taught several courses at both undergraduate and graduate levels. His current research fields of interest include: modeling of cooling techniques related to hot sections in gas turbine engines and electronic components, combined heat transfer (mixed convection–radiation) in channels, turbulent reactive and non-reactive flows, and nano convection heat Transfer.
Saied Moghaddam
Saied Moghaddam received his B.S. and M.S. degrees in the field of Energy Conversion at the Department of Mechanical Engineering, University of Tehran. He is currently a Ph.D. candidate in the Combined Heat Transfer research group of Iran University of Science and Technology. His current research field is focused on turbulence using LES and RANS techniques and various heat transfer phenomena such as thermal radiation, forced, free and mixed convection in various configurations. Also, turbulence-radiation interaction and non-Boussinesq conditions are two of his main studies.
Masoud Aghaamini
Masoud Aghaamini obtained his B.S. degree from University of Kashan, and has completed his M.S. degree in Energy Conversion at the School of Mechanical Engineering, Iran University of Science and Technology, with distinction. His field of research includes turbulence modeling and various heat transfer phenomena such as thermal radiation, forced, free and mixed convection in vertical and horizontal channels. He is planning to continue his studies at Ph.D. level.